The range of the function defined by is the set of such that for some .

One way to determine the range of the function defined by is to solve the equation for and then determine which correspond to at least one . To solve for , first subtract from both sides to get and then take the reciprocal of both sides to get . The equation shows that for any other than , there is an such that , and that there is no such for . Therefore, the range of the function defined by is all real numbers except .

Alternatively, one can reason about the possible values of the term . The expression can take on any value except , so the expression can take on any value except . Therefore, the range of the function defined by is all real numbers except .